Droplets exist widely in our everyday life and various industries. Numerous studies have been done to explore droplet systems and among them Gibbsian surface thermodynamics is a powerful means to investigate these highly curved systems. Due to the development of modern technologies and the introduction of novel materials, new systems have arisen that require this type of investigation. Here we have chosen two multiphase droplet systems of recent interest: the first one is droplet nucleation on a soft substrate as a modern material and the second one is the microdrop concentrating process which is mainly used in microfluidic technologies.
Gibbsian surface thermodynamics is a rigorous method to predict the behaviour of highly curved surfaces such as droplets, bubbles, capillaries or colloid systems. This approach includes finding the conditions for equilibrium and explores the nature of each equilibrium state, i.e., whether it is stable, unstable or metastable. The stability analysis is done by means of free energy calculation and the amount of an energy barrier determines the required energy for nucleation.
In the first system of interest, we provide a mathematical explanation for easier droplet nucleation on a soft substrate compared with a rigid surface, an effect which has been observed experimentally by other researchers. In the second system of interest, we study the microdrop concentrating process which has application in microfluidic microdrop platforms. We provide the first thermodynamic description for microdrop concentrating of two types of solutes—those with and without solubility limits—and explore the role of different design parameters on the equilibrium states. Next we perform thermodynamic stability analysis of the process to determine the behaviour of the system at each equilibrium state. Finally, the role of the Ostwald–Freundlich equation describing the effect of curvature of the precipitated solutes within the microdrops is fully explored.

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